An arbitrary general relativistic world model, i.e., a pseudo‐Riemannian manifold along with a timelike vector field V, is considered. Such a kinematical world model is called ‘‘parallax‐free’’ iff the angle under which any two observers (i.e., integral curves of V) are seen by any third observer remains constant in the course of time. It is shown that a model is parallax‐free iff V is proportional to some conformal Killing field. In this case V, especially, has to be shear‐free. Furthermore a relationship between parallaxes and red shift is presented and a reference is made to considerations concerning the visibility of cosmic rotation.
REFERENCES
1.
2.
3.
4.
W. Rindler, Essential Relativity (Springer, New York, 1977).
5.
M. v. Laue, Das Relativitätsprinzip (Vieweg, Braunschweig, 1911).
6.
J. Ehlers, Akad. Wiss. Lit. (Mainz), Abh. Math. Nat. Kl. 1961 (11), 791.
7.
J.
Ehlers
, P.
Geren
, and R. K.
Sachs
, J. Math. Phys.
9
, 1344
(1968
).8.
J. D.
Barrow
, R.
Juskiewicz
, and D. H.
Sonoda
, Mon. Not. R. Astron. Soc.
213
, 917
(1985
).9.
C. v. Westenholz, Differential Forms in Mathematical Physics (North‐Holland, Amsterdam, 1981).
10.
E. Schrödinger, Expanding Universes (Cambridge U.P., Cambridge, 1956).
11.
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© 1988 American Institute of Physics.
1988
American Institute of Physics
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